Problem: Find the greatest common factor of $44$ and $16$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $44$ and $16$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}44 &=2\cdot2\cdot11\\\\\\\\ 16&=2\cdot2\cdot2\cdot2 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}44 &=2\cdot2\cdot11\\\\\\\\ 16&=2\cdot2\cdot2\cdot2 \end{aligned}$ Each number shares the factors ${2}$ and ${2}$, so the GCF is $2\cdot2=4$. The greatest common factor of $44$ and $16$ is $4$.